Generalized Yamabe Flows
Differential Geometry
2025-09-09 v2
Abstract
In this work we introduce a family of conformal flows generalizing the classical Yamabe flow. We prove that for a large class of such flows long-time existence holds, and the arguments are in fact simpler than in the classical case. Moreover, we establish convergence for the case of negative scalar curvature and expect a similar statement for the positive and the flat cases as well.
Cite
@article{arxiv.2412.02593,
title = {Generalized Yamabe Flows},
author = {Jørgen Olsen Lye and Boris Vertman and Mannaim Gennaro Vitti},
journal= {arXiv preprint arXiv:2412.02593},
year = {2025}
}
Comments
V2: Added some clarification about the potential difference between the background metric and the initial metric. Corrected typos